The charge transfer in semiconductor heterojunction photocatalyst is one of the key factors determining its catalytic efficiency and durability in an aqueous environment. The widely used interface model with the simplified rectangular potential barrier fails to precisely predict the carrier transfer process since the band bending and its variation caused by solar energy are both not considered. Here, utilizing transfer matrix method, we take the Si/TiO₂ heterojunction as a prototype to shed light on the rational design of the semiconductor heterojunction photocatalyst in terms of its intrinsic characteristics, such as TiO₂ thickness and the dopant concentration. We find that the minimum incident energy (MIE) for electrons (holes) tunneling through the Si/TiO₂ heterojunction decreases (increases) as the thickness of TiO₂ layer increases. Within a moderate condition (TiO₂ thickness of 3 nm and dopant concentration of 1 × 10¹⁸ cm⁻³ (5 × 10¹⁹ cm⁻³) in Si (TiO₂)), both electrons and holes can transfer through the heterojunction barrier with relatively small incident energy. Furthermore, the photovoltage under illumination is beneficial for reducing MIE for electrons while increasing that for holes. Therefore, our transfer matrix scheme provides insights into rational design of the high efficient photocatalyst.

中文翻译：

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Si / TiO ₂异质结光催化剂的合理设计：转移矩阵法

半导体异质结光催化剂中的电荷转移是决定其在水性环境中的催化效率和耐久性的关键因素之一。广泛使用的具有简化的矩形势垒的界面模型无法精确预测载流子传输过程，因为未同时考虑由太阳能引起的频带弯曲及其变化。在本文中，我们采用转移矩阵法，以Si / TiO ₂异质结为原型，就其固有特性（如TiO _2的厚度和掺杂剂的浓度）阐明了半导体异质结光催化剂的合理设计。我们发现，通过Si / TiO ₂隧穿的电子（空穴）的最小入射能（MIE）随着TiO ₂层厚度的增加，异质结减少（增加）。在中等条件下（TiO _2的厚度为3 nm，Si（TiO ₂）中的掺杂剂浓度为1×10 ¹⁸  cm ^-3（5×10 ¹⁹  cm ^-3）），电子和空穴都可以通过异质结势垒转移相对较小的入射能量。此外，光照下的光电压有利于降低电子的MIE，同时提高电子的MIE。因此，我们的转移矩阵方案为高效光催化剂的合理设计提供了见识。